Hi Newman
It's not an uncommon question, and I was actually sorting out a question just like this for a colleague the other day - hence the rapid answer.
You've got two solutions open to you: wireless or wired.
The wireless system could be done with something like the new KEF Wireless system we covered in the June issue of the magazine, which comprises a two-channel sender unit and a pair of receivers with built-in 50W amps. These would work fine with your home cinema system, fed from the rear channel pre-outs of your AV receiver, and with the remote transmitters connected to your rear speakers. The cost? About £400 for a transmitter and a pair of receivers.
However, given that you have a biamped main audio system - I assume the two systems are totally separate - it sounds like you've invested quite a bit in the set-up, so the KEFs probably wouldn't be suitable for the stereo rig.
Instead, I'd suggest taking the opportunity of having the new carpet laid to put flat (or near-flat) cables designed for under-carpet use across the room, or around the edges, to carry speaker signals where you want them.
Suitable cables would include QED's Qontour, which is just 1.7mm thick, and costs around £2/m.
To keep the installation tidy, you could use speaker socket boxes from the QED AveQ Wallmount range: these fit into standard flush-mount or surface-mount boxes, just like mains sockets or light-switches, come in a range of finishes including white and metal, and could be used with the cables chased into the wall, or just surface-mounted at floor/skirting-board level. They have standard 4mm banana sockets, into which you could connect flying leads - short runs of cable - to your speakers
A two-socket box - ie for a single 'red and black' pair of connections - is about £12 or so, and a four-socket about twice as much.
So. (deep breath) you could use a four-socket box somewhere behind your AV receiver, with flying leads from the rear left/right speaker outputs, and cables run across the room under the carpet to two-socket boxes close to the position of your rear speakers.
Similarly, your biamped main speakers could be handled with two four-connector boxes behind your main system rack, connected to a two more four-connector boxes, one close to each of your main speakers.
However, you might think that, while this solution is fine for your rear speakers, it involves just too many plugs and sockets for the best sound from your main system. An alternative would be to lay a high-quality flat biwire cable across the room under the carpet from your audio system to each of the stereo speakers, with cables emerging from under the carpet behind the main system and behind each speaker.For this, something like The Chord Company's Carnival Silver Biwire Plus would do the job very well indeed. It's only 6mm thick, costs about £9.50 a metre, and the single-wire version was a 2004 Award winner.
Here's a few contacts to be going on with - happy cabling and carpet-laying!
QED Wall Sockets
QED Qontour
The Chord Company